DLMF:10.65.E9 (Q3842): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(5 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Kelvin function / rank
 
Normal rank
Property / Symbols used: Kelvin function / qualifier
 
test:

bei ν ⁡ ( x ) Kelvin-bei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

\Kelvinbei{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Kelvin function / qualifier
 
xml-id: C10.S61.E1.m3ahdec
Property / Symbols used
 
Property / Symbols used: Kelvin function / rank
 
Normal rank
Property / Symbols used: Kelvin function / qualifier
 
test:

ber ν ⁡ ( x ) Kelvin-ber 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

\Kelvinber{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Kelvin function / qualifier
 
xml-id: C10.S61.E1.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5ahdec
Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11435 / rank
 
Normal rank
Property / Symbols used: Q11435 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
 
xml-id: C10.S1.XMD4.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1ddec

Latest revision as of 14:23, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.65.E9
No description defined

    Statements

    test
    ( ber ν ′ ⁡ x ) 2 + ( bei ν ′ ⁡ x ) 2 = ( 1 2 ⁢ x ) 2 ⁢ ν - 2 ⁢ ∑ k = 0 ∞ 2 ⁢ k 2 + 2 ⁢ ν ⁢ k + 1 4 ⁢ ν 2 Γ ⁡ ( ν + k + 1 ) ⁢ Γ ⁡ ( ν + 2 ⁢ k + 1 ) ⁢ ( 1 4 ⁢ x 2 ) 2 ⁢ k k ! . superscript diffop Kelvin-ber 𝜈 1 𝑥 2 superscript diffop Kelvin-bei 𝜈 1 𝑥 2 superscript 1 2 𝑥 2 𝜈 2 superscript subscript 𝑘 0 2 superscript 𝑘 2 2 𝜈 𝑘 1 4 superscript 𝜈 2 Euler-Gamma 𝜈 𝑘 1 Euler-Gamma 𝜈 2 𝑘 1 superscript 1 4 superscript 𝑥 2 2 𝑘 𝑘 {\displaystyle{\displaystyle\left(\operatorname{ber}_{\nu}'x\right)^{2}+\left(% \operatorname{bei}_{\nu}'x\right)^{2}=(\tfrac{1}{2}x)^{2\nu-2}\sum_{k=0}^{% \infty}\frac{2k^{2}+2\nu k+\frac{1}{4}\nu^{2}}{\Gamma\left(\nu+k+1\right)% \Gamma\left(\nu+2k+1\right)}\frac{(\frac{1}{4}x^{2})^{2k}}{k!}.}}
    0 references
    DLMF id
    DLMF:10.65.E9
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2addec
    0 references
    Kelvin function
    test
    bei ν ⁡ ( x ) Kelvin-bei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E1.m3ahdec
    0 references
    Kelvin function
    test
    ber ν ⁡ ( x ) Kelvin-ber 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E1.m2ahdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5ahdec
    0 references
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1gdec
    0 references
    Q11435
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1hdec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1ddec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q3842&oldid=20444"